# Variational Regularization of Inverse Problems for Manifold-Valued Data

arXiv: https://arxiv.org/abs/1804.10432 · HTML: https://mlsanity.com/paper/1804.10432/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2018.

## Built on by (most cited first, 2 of 2)

- [A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold](https://mlsanity.com/paper/2302.08210/) (2023)
- [Tikhonov Regularization of Circle-Valued Signals](https://mlsanity.com/paper/2108.02602/) (2021)

## Abstract (arXiv)

In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide results on the well-posedness and present algorithms for a numerical realization of these models in the manifold setup. Further, we provide experimental results for synthetic and real data to show the potential of the proposed schemes for applications.